# How do you solve 3/4 = 3/8x - 3/2?

Jul 13, 2015

My first step would be to multiply everything on both sides by $8$ to get rid of all the fractions.

#### Explanation:

$\to 6 = 3 x - 12 \to 18 = 3 x \to x = 6$

Jul 13, 2015

I found: $x = 6$

#### Explanation:

I would take $8$ as common denominator and write:
$\frac{\textcolor{red}{2} \cdot 3}{8} = \frac{3 x}{8} - \frac{\textcolor{red}{4} \cdot 3}{8}$
where the red terms were introduced to adapt the numerators to the new denominator $8$.
I can now get rid of the denominators and get:
$\frac{2 \cdot 3}{\cancel{8}} = \frac{3 x}{\cancel{8}} - \frac{4 \cdot 3}{\cancel{8}}$
$6 = 3 x - 12$
and:
$3 x = 18$
$x = \frac{18}{3} = 6$

Jul 13, 2015

$x = 6$

#### Explanation:

OK, we are given $\frac{3}{4} = \frac{3}{8} x - \frac{3}{2}$

First, let's add $\frac{3}{2}$ to both sides:

$\frac{3}{4} = \frac{3}{8} x - \frac{3}{2}$

$\frac{3}{4} + \frac{3}{2} = \frac{3}{8} x$

We need a common denominator for both $\frac{3}{4}$ and $\frac{3}{2}$, so we'll go with the common denominator of $4$, since both $2$ and $4$ go into $4$:

$\frac{3}{4} + \frac{3}{2} = \frac{3}{8} x$

$\frac{3}{4} + \frac{2 \cdot 3}{2 \cdot 2} = \frac{3}{8} x$

$\frac{3}{4} + \frac{6}{4} = \frac{3}{8} x$

Now, add $\frac{3}{4} + \frac{6}{4}$ to get $\frac{9}{4}$

$\frac{3}{4} + \frac{6}{4} = \frac{3}{8} x$

$\frac{9}{4} = \frac{3}{8} x$

Now, multiply both sides by the reciprocal of $\frac{3}{8}$ which is $\frac{8}{3}$

$\frac{9}{4} = \frac{3}{8} x$

$\frac{8}{3} \cdot \frac{9}{4} = \frac{8}{3} \cdot \frac{3}{8} x$

$\frac{2}{1} \cdot \frac{3}{1} = 1 \cdot x$

$2 \cdot 3 = x$

$6 = x$